STAT302: Secs 102 & 103Summer I 1998Exam #3Fo r m AInstructor: Julie Hagen Carroll1. Don’t even open this until you are told to do so.2. Be sure to mark your section number (102 or 103) and your test form (A or B) on the scantron!3. Sign your name where indicated on your scantron and write your Wednesday section number andcomputer number beside it. Also, you must place your scantron in the correct section stack (for nextWednesday).4. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Pleasemark your answers clearly on the scantron. Multiple marks will be counted wrong.5. You will have 60 minutes to finish this exam.6. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade ofzero on the exam. You must work alone.7. This exam is worth 100 points, and will constitute 20% of your final grade.8. Good luck!1STAT302: 102 & 103 Exam #3, Form A Summer 19981. What are H0and HAfor the graph above?A. H0: µ1= µ2vs. HA: µ16= µ2B. H0: µ1=0vs. HA: µ16=0C. H0: µ1=0vs. HA: µ2=0D. H0: µ =0vs. HA: µ 6=0E. H0: µ1= µ2vs. HA: µ1>µ22. Suppose you feel certain that for the last 10 yearsAggie graduates made more money than t-sipsin their first year out of college. Which of thefollowing would be the best method for testingthis hypothesis?A. Ask 10 Aggies and 10 t-sips how muchthey make and compare the averages.B. Collect random samples of graduating se-niors from both schools and compare theiraverage job offers.C. Collect random samples of people whograduated in the last 10 years from bothschools and compare the proportions ofsalaries over $30,000 for each school.D. Collect random samples of people whograduated in the last 10 years from bothschools and compare their average startingsalaries.E. Collect random samples of graduating se-niors from both schools and compare theproportions of salaries over $30,000 for eachschool.3. What would be the consequence of making aType II error in the situation above?A. You claim that Aggie first year graduatesmake more than t-sips when they do notmake more.B. You do not claim that Aggie first year grad-uates make more than t-sips when they donot make more.C. You claim that Aggie first year graduatesmake more than t-sips when they do makemore.D. You do not claim that Aggie first year grad-uates make more than t-sips when they domake more.E. You claim that Rice Owls make the mostmoney.4. If t.u. found out about your hypothesis test be-fore you collected any data, which α level wouldthey want you to use? Assume that they don’twant you to conclude that Aggies make moremoney.A. 0.01B. 0.05C. 0.10D. It doesn’t matter since we know that Aggiesmake more.E. They don’t care since they don’t under-stand hypothesis testing.5. Still talking about Aggies and t-sips andsalaries, which type test (case) should you useif you don’t know anything about the means orthe standard deviations of either school?A. Case 1 because it is the most basic type oftest.B. Case 3 because we don’t know that the datais normal nor the standard deviation.C. Case 6 because comparing the proportionswould mean we don’t have to have the samesample sizes.D. Case 9 because we don’t know that the datais normal nor either standard deviation oreven if they’re equal.E. Case 11 because we should compare twoproportions.2STAT302: 102 & 103 Exam #3, Form A Summer 19986. Ok, suppose that the true mean starting salaryfor Aggies is $40,000 with a standard deviation of$1500 and that of t-sips is $30,000 and $2000,respectively. What is the distribution of the dif-ference in sample means based on samples of size100?A. N(10, 000, 52)B. N(10, 000, 5002)C. N(10, 000, 2502)D. N(10, 000, 25002)E. N (70, 000, 5002)7. What is the significance level, α?A. the probability of rejecting the null hypoth-esisB. a measure of how willing we are to make aType I errorC. the proportion of times we will reject a trueH0D. all of the aboveE. exactly two of the above (excluding D.)8. Suppose we generate 50 random samples from apopulation of N(4, 102). From these samples, wecreate 50 95% confidence intervals. If we look atall of our confidence intervals collectively, thenA. no more than 95% of them will contain thetrue mean of 4.B. exactly 95% of them will contain the truemean of 4.C. approximately 95% of them will contain thetrue mean of 4.D. approximately 95% of them will contain thesample mean, x.E. Exactly twoof the above are correct.9. If we had calculated 90, 95 and 99% confidenceintervals using the data above, which of the fol-lowing would be true?A. 0 would be in all three confidence intervalsB. 25 would be in all three confidence intervalsC. 25 would not be in any of the three confi-dence intervalsD. 25 would not be in the 90 or 95%, but itwould fall within the 99% confidence inter-valE. 0 would not be in the 90 or 95%, but itwould fall within the 99% confidence inter-val10. Suppose we know that we rejected at the 5% αlevel. Which of the following do we also know?A. We would have also rejected at the 1% level.B. We don’t know if we would have rejected atthe 10% level.C. The hypothesized value (e.g., µ0)wouldbein a 95% confidence interval for µ.D. All of the above would be true.E. None of the above would be true.3STAT302: 102 & 103 Exam #3, Form A Summer 199811. Suppose we tested H0: µ =50vs. HA: µ<50.The p-value for our sample was 0.026. Which ofthe following is the best definition of what thep-value is saying?A. There is 2.6% likelihood of getting a samplemean at least as large as our sample meaneven though the true population mean is 50.B. There is 2.6% likelihood of getting a samplemean at least as small as our sample meaneven though the true population mean is 50.C. There is 2.6% likelihood of getting the samesample mean as our sample mean eventhough the true population mean is 50.D. There is 2.6% likelihood of getting a sam-ple mean less than 50 even though the truepopulation mean is 50.E. There is 2.6% likelihood of getting a sam-ple mean equal to 50 even though the truepopulation mean less than 50.Variable |Obs Mean Std.Err. [Conf. Interval]---------+--------------------------------------90% | 25 18 1.2 15.94694 20.0530695% | 25 18 1.2 15.52332 20.4766899% | 25 18 1.2 14.64367 21.3563312. Suppose we want to test H0: µ =21vs. HA:µ 6= 21. Using the confidence intervals above,what would be the range of the p-value for thistest?A. pv> 0.10B. 0.10 >pv> 0.05C. 0.05 >pv> 0.01D. 0.01 >pvE. 21 <pv13. Suppose